P10 - Also, do the following additional problems. A. True...

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Math 141, Problem Set #10 (due in class Fri., 11/21/11) Note: To get full credit for a problem, it is not enough to give the right answer; you must explain your reasoning. Stewart, section 4.1, problems 4, 24, 28, 32, 36, 38, 44, 48, 56, 62. (For prob- lem 4.1.62, your reasoning should use the definition of maxima and minima. Also note that you cannot assume that the function is differentiable, since this is not part of the statement of the problem, so Fermat’s Theorem etc. are not relevant. You should not even assume that f is continuous!) Stewart, section 4.2, problems 6, 12, 16, 22, 24, 26, 27, 29. You are to solve problem 27 using the result of problem 26, and not by using algebra or some other method.
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Unformatted text preview: Also, do the following additional problems. A. True or false? (and why?): If f is continuous on a closed interval [ a,b ], then f attains a local maximum value f ( c ) and a local minimum value f ( d ) at some numbers c and d in [ a,b ]. B. Show that the function 2 x + sin x is invertible. (Hint: To show that the function f ( x ) = 2 x + sin x is invertible, rst use f ( x ) to show that f ( x ) is an increasing function.) Please dont forget to write down on your assignment who you worked on the assignment with (if nobody, then write I worked alone), and write down on your time-sheet how many minutes you spent on each problem (this doesnt need to be exact)....
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